Here \(H\)  denotes an unconstrained gauge prepotential for conformal supergravity.
Modulo purely gauge degrees of freedom,
the structure of unconstrained conformal gauge prepotentials are as follows:
\(H_{\alpha \beta \gamma } \) 
for \({\cal N}=1\)  [1]}, \(H_{\alpha \beta }\)  for \({\cal N}=2\)  [2]}, [3]},
\(H_\alpha \)  for \({\cal N}=3\)  [4]}, and \(H\)  for \({\cal N}=4\)  [4]}.
